However, hanging from it an appendage in the atmosphere (that lovely figure-8 pattern) will sap the asteroid's energy, leading, sooner or later, to asteroid orbital decay and reverse high-rise disaster.
Of course, this might be fixed by boosting the asteroid, but that's another calculation (or did I miss it from the link?).
Oh, and assuming the energy and physics can be made to work, it should be interesting to have one's office whisked about in that analemma at airliner speeds.
Don’t open the window..................